Certainly! Let's subtract the two algebraic expressions step-by-step.
Given:
[tex]\[ (7y + 8) - (4y + 5) \][/tex]
We'll follow these steps:
1. Distribute the subtraction sign through the second set of parentheses.
2. Combine like terms.
### Step 1: Distribute the subtraction sign
When we distribute the subtraction sign through the second parentheses, it reverses the sign of each term inside the parentheses:
[tex]\[ 7y + 8 - 4y - 5 \][/tex]
### Step 2: Combine like terms
Now, we combine like terms. Like terms are terms that contain the same variables raised to the same power. In this case, the like terms are [tex]\( 7y \)[/tex] and [tex]\( -4y \)[/tex], and the constants [tex]\( 8 \)[/tex] and [tex]\( -5 \)[/tex]:
- Combine [tex]\( 7y \)[/tex] and [tex]\( -4y \)[/tex]:
[tex]\[ 7y - 4y = 3y \][/tex]
- Combine the constants [tex]\( 8 \)[/tex] and [tex]\( -5 \)[/tex]:
[tex]\[ 8 - 5 = 3 \][/tex]
### Final Expression
Putting our combined results together, we have:
[tex]\[ 3y + 3 \][/tex]
So, the simplified result of subtracting [tex]\( (4y + 5) \)[/tex] from [tex]\( (7y + 8) \)[/tex] is:
[tex]\[ 3y + 3 \][/tex]
